The picadilly line will get you to London on the cheap.. but its slow. With only 7 hours to kill, bite the $$ and take the heathrow express (or whatever its called) which takes you into town in 15 minutes or so. It dumps out at one of the main rail stations in SW London, from there you can take a short tube/bus/funny cab ride to where ever you want to go.. total time about 30 minutes in each direction.
I would say with that time you could easily see the sights of one part of central london (st james park/big ben/buckingham palace/the thames as one example), or hit up oxford street, soho, the british museum (see egyptian mummies up close and personal - yikes!), or go on further down and explore the tower of london... all fun stuff!